演讲专家： Michael Winkler, University of Paderborn
演讲主题： Mathematical challenges arising in the analysis of chemotaxis-fluid interaction
报告摘要：We consider models for the spatio-temporal evolution of populations of microorganisms, moving in an incopressible fluid, which are able to partially orient their motion along gradients of a chemical signal. According to modeling approaches accounting for the mutual interaction of the swimming cells and the surrounding fluid, we study study parabolic chemotaxis systems coupled to the (Navier-)Stokes equations through transport and buoyancy-induced forces.The presentation discusses mathematical challenges encountered even in the context of basic issues such as questions concerning global existence and boundedness, and attempts to illustrate this by reviewing some recent developments. A particular focus will be on strategies toward achieving a priori estimates which provide information sufficient not only for the construction of solutions, but also for some qualitative analysis.